HardyWeinberg equilibrium

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Hardy-Weinberg equilibrium
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Hardy-Weinberg equilibrium
Is this a true population or a mixture? Is the
population size dangerously low? Has migration
occurred recently? Is severe selection occurring?
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa N alleles
Genotype frequency
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa N 50
alleles 100 Genotype frequency 202010
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa N 50
alleles 100 Genotype frequency
202010 Allelic frequencies A a
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa N 50
alleles 100 Genotype frequency
202010 Allelic frequencies A red (20
20) pink (20) 60 (or 0.6) a white (10
10) pink (20 ) 40 (or 0.4)
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Quantifying genetic variation Genotype
frequencies red flowers 20 homozygotes
AA pink flowers 20 heterozygotes Aa white
flowers 10 homozygotes aa N 50
alleles 100 Genotype frequency
202010 Allelic frequencies A red (20
20) pink (20) 60 p a white (10 10)
pink (20 ) 40 q
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Reduce these frequencies to proportions Genotype
frequencies AA 20 or 0.4 Aa 20
0.4 aa 10 0.2 Allelic frequencies A
p 0.6 a q 0.4
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Check that proportions sum to 1 Genotype
frequencies AA 20 or 0.4 Aa 20
0.4 AA Aa aa 1 aa 10 0.2 Allelic
frequencies A p 0.6 p q 1
a q 0.4
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Genotype frequencies AA 20 or 0.4
Aa 20 0.4 AA Aa aa 1 aa 10
0.2 Allelic frequencies A p 0.6
p q 1 a q 0.4 If we combined the
alleles at random (per Mendel), then
genotype frequencies would be predictable by
multiplicative rule AA Aa aa
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Genotype frequencies AA 20 or 0.4
Aa 20 0.4 AA Aa aa 1 aa 10
0.2 Allelic frequencies A p 0.6
p q 1 a q 0.4 If we combined the
alleles at random (per Mendel), then
genotype frequencies would be predictable by
multiplicative rule AA p x p p2 Aa p x
q x 2 2pq aa q x q q2
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Genotype frequencies AA 20 or 0.4
Aa 20 0.4 AA Aa aa 1 aa 10
0.2 Allelic frequencies A p 0.6
p q 1 a q 0.4 If we combined the
alleles at random (per Mendel), then
genotype frequencies would be predictable by
multiplicative rule AA p x p p2 0.36 Aa
p x q x 2 2pq 0.48 aa q x q q2
0.16
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Genotype frequencies AA 20 or 0.4
Aa 20 0.4 AA Aa aa 1 aa 10
0.2 Allelic frequencies A p 0.6
p q 1 a q 0.4 If we combined the
alleles at random (per Mendel), then
genotype frequencies would be predictable by
multiplicative rule AA p x p p2 0.36 Aa
p x q x 2 2pq 0.48 aa q x q q2
0.16
check sum of the three genotypes
must equal 1
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AA p x p p2 0.36 Aa p x q x 2 2pq
0.48 aa q x q q2 0.16 Thus,
frequency of genotypes can be expressed as p2
2pq q2 1
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AA AA Aa p, q Aa aa aa
parental generation gamete
offspring (F1) genotypes
frequencies genotypes
reproduction
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Hardy-Weinberg (single generation)
observed allele expected genotypes
frequencies genotypes
AA AA Aa p, q Aa aa aa
calculated deduced
parental generation gamete
offspring (F1) genotypes
frequencies genotypes
reproduction
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Why would genotype frequencies ever NOT be the
same as predicted from the allele frequencies?
observed expected
AA AA Aa p, q Aa aa aa
calculated deduced
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Hardy-Weinberg equilibrium Observed genotype
frequencies are the same as expected frequencies
if alleles combined at random
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Hardy-Weinberg equilibrium Observed genotype
frequencies are the same as expected frequencies
if alleles combined at random Usually true if -
population is effectively infinite - no
selection is occurring - no mutation is
occurring - no immigration/emigration is
occurring
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How do we evaluate all this???? (how close
must the data be to the ratios?)
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How do we evaluate all this???? (how close
must the data be to the ratios?)
genotype observed expected
AA 19 Aa 57 aa 24 total 100
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How do we evaluate all this???? (how close
must the data be to the ratios?)
p (219 57)/200 0.475 q (57 224)/200
0.525
genotype observed expected
AA 19 Aa 57 aa 24 total 100
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How do we evaluate all this???? (how close
must the data be to the ratios?)
p (219 57)/200 0.475 q (57 224)/200
0.525
genotype observed expected
AA 19 22.5 Aa 57 50 aa 24
27.5 total 100 100
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How do we evaluate all this???? (how close
must the data be to the ratios?) Chi square
?2 (observed expected)2
expected
?
dev. from exp.
(obs-exp)2 genotype observed expected
(obs-exp) exp AA 19
22.5 Aa 57 50 aa 24 27.5 total 100
100
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How do we evaluate all this???? (how close
must the data be to the ratios?) Chi square
?2 (observed expected)2
expected
?
dev. from exp.
(obs-exp)2 genotype observed expected
(obs-exp) exp AA 19
22.5 -3.5 0.54 Aa 57 50
7 0.98 aa 24 27.5 -2.5 0.45 total 100
100 1.97 ?2
degrees of freedom 2 ( N 1)
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P gt0.25 (observed data not significantly
different) from expected data)